Beyond Routing: Characterising Expert Tuning and Representation in Vision Mixture-of-Experts

Technical Summary: Beyond Routing: Characterising Expert Tuning and Representation in Vision Mixture-of-Experts

Problem Statement
Mixture-of-Experts (MoE) models are increasingly prevalent in deep learning, offering interpretability through the partitioning of tasks into distinct subnetworks (experts). However, current interpretability efforts in vision MoEs are predominantly limited to analyzing routing statistics (e.g., gating weights, token-to-expert assignments, or class-based heatmaps). The authors argue that routing decisions serve as a proxy for specialization but fail to reveal what the experts actually encode. Existing literature often assumes experts are tuned to discrete semantic categories (e.g., "animals" or "vehicles") based solely on which inputs they receive. This approach overlooks the internal feature-tuning profiles and the representational geometry of the experts themselves, leaving the nature of expert specialization poorly understood.

Methodology
To address this, the authors trained sparsely-gated convolutional MoE models (MoE-CNNs) using a self-supervised contrastive objective (NT-Xent loss) on the unlabeled STL10 dataset. This training regime avoids baking predefined categorical structures into the learning signal, allowing data-driven visual feature specialization to emerge naturally.

• Architecture: The model utilizes a ResNet backbone where the first three blocks are shared. A gating network then routes inputs to $k=2$ experts selected from a pool of $E \in \{4, 8, 16\}$ experts. To control for parameter count, the channel width of experts is scaled by $1/\sqrt{E}$, ensuring the total parameter count remains constant (~46M) across configurations.
• Analysis Tools: The study extends analysis from gating-level to expert-level and from category-level to feature-level using tools from visual neuroscience:
  1. Most Exciting Inputs (MEIs): Visualizing inputs that maximize the $L_2$ norm of an expert's readout embedding.
  2. THINGS Dataset: Using the THINGS dataset (1,854 object concepts) and its associated THINGS Similarity dataset (66 human-behavior-derived visual and semantic dimensions) as an out-of-distribution (OOD) probe.
  3. Regression Analysis: Fitting non-negative Lasso regressions to predict gating logits and readout magnitudes from the 66 THINGS dimensions to identify continuous tuning profiles.
  4. Representational Similarity Analysis (RSA): Computing pairwise category separability and second-order RSA to assess the stability of representational geometries across 10 independently trained models (different random seeds).

Key Contributions

1. Beyond Routing: The authors demonstrate that routing statistics systematically mischaracterize expert encoding. They show that while routing suggests sparse, categorical preferences, the actual expert tuning is broader and driven by continuous dimensions.
2. Beyond Categories: By leveraging the THINGS dataset, the study disentangles expert tuning from the categorical structure of the training set. It recovers interpretable, continuous tuning profiles based on semantic and visual dimensions (e.g., "metallic," "spiky," "animal-related") rather than discrete classes.
3. Representational Stability: The paper identifies that specific representational motifs (particularly the animate-inanimate distinction) re-emerge reliably across independent model initializations, suggesting these are robust organizational principles rather than random artifacts.

Results

• Routing vs. Tuning Divergence: Routing analyses on the STL10 test set suggested experts specialized in coarse categories (e.g., trucks, birds). However, MEI analysis and regression on the THINGS dataset revealed that experts were often tuned to low-level image statistics (e.g., graininess, spatial frequency) or specific continuous features (e.g., "metallic," "repetitive/spiky") that did not align with the categorical labels suggested by routing.
• Gating vs. Readout Mismatch: There was no linear relationship between gating logits (what is routed to an expert) and readout activation magnitudes (what the expert actually encodes). Experts transform their routed inputs, discovering and amplifying features distinct from those used for routing.
• Dominance of Animacy: Despite diverse feature tuning, a binary animate-inanimate distinction dominated expert partitioning. This was evident in gating, readout, and representational geometry. This split was stable across all model configurations ($E=4, 8, 16$) and independent initializations.
• Shared Geometry, Distinct Implementation: While experts exhibited distinct feature tuning (MEIs), their representational geometries (category separability) were strikingly similar. This indicates that functionally equivalent category-level structures can be realized through distinct population-level response patterns.

Significance and Claims
The paper claims that expert specialization in vision MoEs is better understood not as sparse tuning to discrete categorical classes, but as sparse tuning to continuous, behaviorally relevant dimensions.

• Reframing Interpretability: The authors argue that moving beyond routing to probe fine-grained expert-level tuning and representational structure provides a more accurate picture of what MoEs learn.
• Neuroscientific Parallel: The findings align with contemporary accounts of distributed tuning in the human ventral visual cortex, where "expert" areas (like the FFA or PPA) are broadly sensitive to continuous dimensions (e.g., animacy, size, texture) rather than being purely category-selective.
• Stability: The recovery of the animate-inanimate partition across independent runs suggests that visual systems (both biological and artificial) are constrained by the statistical structure of natural images, leading to consistent organizational axes.

The authors remain modest regarding the scope, noting that their findings are based on self-supervised learning on a relatively small dataset (STL10) and that results might differ with larger-scale industrial MoEs or different training objectives. However, they posit that MoE models offer a computational framework for investigating why visual features are distributed across the cortex as they are.